… or why we know there is a greenhouse effect, and it doesn’t easily saturate.

First, let’s figure out what the magnitude of the incoming solar radiation is at any point from a star. This example is limited to systems with only one star. That star will emit radiation according the the Stefan–Boltzmann law:

Because of conservation of energy the energy flowing through a sphere equal to the radius of the sun and a sphere equal to the star-planet distance (X_p). Actually, it needs to be equal for all such surfaces that enclose the star. Because it flows through the surface area, there is a factor of 4π that I’ve already cancelled on both sides of the equation.

Now let’s solve for I_p while substituting the expression for I_sun.

I’ve already solved for the effective temperature of an object based on its albedo (related to the emissivity) and the incident intensity, see for example Falsification Of The Atmospheric CO2 Greenhouse Effects.

Now simply substituting in for I_p in the above equation using our derived expression about we get

Let’s plug in some values. The sun has a temperature of about 5800K. To get an upper bound on the effective temperature of Venus, assume the albedo (A) is zero. After solving the equation, we end up with a value of 329K (56C) for the effective temperature. Now let’s assume that the surface of Venus is composed of such a material that it has an albedo of 0.4 and there are no clouds (this is not true). In this case, Venus would have an effective temperature of 290K (17C). Actually, Venus has an albedo of around 0.77, which gives an effective temperature of 227K (-46C). Brrrr. Clearly, the effective temperature is highly dependent upon the albedo of the planet. The effective temperature of Venus is lower than that of Earth even though it is closer to the sun because of its high albedo.

Why do we care what the effective temperature is on Venus? Because the difference between the effective temperature and the actual surface temperature can help elucidate the greenhouse effect.

The atmosphere of Venus is about 96% carbon dioxide by volume. [Chaisson and McMillan, 1997] This makes it the most important greenhouse gas - for Venus. Not only does the composition of Venus’ atmosphere differ from Earth’s, the amount of atmosphere does too. Venus has about surface pressure about 90 times that of Earth’s. In fact, the greenhouse effect on Venus has been known since 1969 [Ingersol, 1969]

References:
• Chaisson, Eric and McMillan, Steve, Astronomy Today, 2nd Ed., Prentice-Hall, (1997).
• Ingersoll, A.P., 1969. The runaway greenhouse: A history of water on Venus. J. Atmos. Sci. 26 (1969), 1191-1198.

(No Ratings Yet)

 Loading ...

Related Posts:

Trackback URI |